Answer
(a) If εε is the set 1,2,3,…,19,201,2,3,…,19,20 and A, B and C are subsets of εε such that A = { multiples of five}, B = {multiples of four} and C = {multiples of three}, list the elements of (i) A ; (ii) B ; (iii) C ;
(b) Find : (i) A∩BA∩B ; (ii) A∩CA∩C ; (iii) B∪CB∪C.
(c) Using your results in (b), show that (A∩B)∪(A∩C)=A∩(B∪C)(A∩B)∪(A∩C)=A∩(B∪C).
Answer
(a)(i) A = {5, 10, 15, 20}
(ii) B = {4, 8, 12, 16, 20}
(iii) C = {3, 6, 9, 12, 15, 18}
(b) (i) A∩B=20A∩B=20
(ii) A∩C=15A∩C=15
(iii) B∩C=12B∩C=12
(c) (A∩B)∪(A∩C)=A∩(B∪C)
(A∩B)∪(A∩C)=15,20
A∩(B∪C)=5,10,15,20
∩3,4,6,8,9,12,15,16,18,20
∴ (A∩B)∪(A∩C)=A∩(B∪C)
ABC is a triangle, right-angled at C. P is the mid-point of AC, < PBC = 37° and |BC| = 5 cm. Calculate :
(a) |AC|, correct to 3 significant figures ;
(b) < PBA.
Answer
Answer
Let |PC| = x cm; Hence, |AC| = 2x cm
tan37° = x5tan 37°=x5
x = 5tan 37
x = 3.768cm
∴ |AC|= 2×3.768
= 7.536cm
≊7.54cm (3 sig. figs)
(b) From ΔABC,
tan < ABC= 7.536 / 5 = 1.5072
<ABC = tan−1(1.5072)=56.436°
∴< PBA = <ABC − <PBC
= 56.436°−37°
= 19.436°≊19.44°
In the diagram, ABCD is a trapezium in which AD∥BCAD∥BC and <ABC<ABC is a right angle. If |AD| = 15 cm, |BD| = 17 cm and |BC| = 9 cm, calculate :
(a) |AB| ;
(b) the area of the triangle BCD ;
(c) |CD| ;
(d) perimeter of the trapezium.
Answer
